In the present paper, various wave solutions of a novel KP-like equation were successfully derived, on the basis of Hirota bilinear method. First, multi-breather wave solutions including one-brather wave, two-breather wave, three-breather wave and hybrid solutions between breather waves and solitary waves have been constructed with their dynamic characters and physical structure via choosing the complex conjugate parameter values. Next, by combining the long wave limit method and choosing the complex conjugate parameter values in term of multi-kink solutions, multi-lump wave solutions including one-lump wave, two-lump wave and three-lump wave and two types of hybrid solutions between lump waves and solitary waves have been obtained. Additionally, the one-breather wave and one-lump wave have been studied in detail. Finally, several groups of images exhibited their trajectories and the fusion and fission process with physical interpretion via symbolic computation. Furthermore, the obtained results have immensely enriched the exact solutions of a novel KP-like equation on the available literature and enabled us to understand the nonlinear dynamic system deeply.